<h2>Problem 246</h2>
<div style="color:#666;font-size:80%;">22 May 2009</div><br />
<div class="problem_content">
<p>
A definition for an ellipse is:<br />
Given a circle c with centre M and radius r and a point G such that d(G,M)<img src='images/symbol_lt.gif' width='10' height='10' alt='&lt;' border='0' style='vertical-align:middle;' />r, the locus of the points that are equidistant from c and G form an ellipse.
</p>
The construction of the points of the ellipse is shown below.
</p>
<div style="text-align:center;">
<img src="project/images/p_246_anim.gif" alt="" /></div>

<p>
Given are the points M(-2000,1500) and G(8000,1500).<br /> 
Given is also the circle c with centre M and radius 15000.<br />
The locus of the points that are equidistant from G and c form an ellipse e.<br />
From a point P outside e the two tangents t<img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" /> and t<img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" /> to the ellipse are drawn.<br />
Let the points where t<img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" /> and t<img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" /> touch the ellipse be R and S.
</p>
<div style="text-align:center;">
<img src="project/images/p_246_ellipse.gif" alt="" /></div>
<p>
For how many lattice points P is angle RPS greater than 45 degrees?
</p>

</div><br />
